Internal problem ID [2328]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 37, page 171
Problem number: 15.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}+y^{2}=1} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 29
dsolve(diff(y(x),x)^2+y(x)^2=1,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -1 \\ y \left (x \right ) &= 1 \\ y \left (x \right ) &= -\sin \left (c_{1} -x \right ) \\ y \left (x \right ) &= \sin \left (c_{1} -x \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.175 (sec). Leaf size: 39
DSolve[y'[x]^2+y[x]^2==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cos (x+c_1) \\ y(x)\to \cos (x-c_1) \\ y(x)\to -1 \\ y(x)\to 1 \\ y(x)\to \text {Interval}[\{-1,1\}] \\ \end{align*}